 Mathematics
24 June, 05:09

# The length of a rectangle is two more than four times the width if the perimeter is 54 inches what are the length and width?

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1. 24 June, 06:59
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Length = 22 inches, Width = 5 inches

Step-by-step explanation:

Let P represent the Perimeter, L, the length and W, the width

Perimeter of a rectangle, P = 2 (L + W) ... eq 1

from the question;

L = 2 + 4W ... eq 2

Slotting in the respective values of P and L in eq 1

54 = 2{ (2 + 4W) + W}

Expanding the bracket

54 = 2 (2 + 5W)

54 = 4 + 10W

Subtracting 4 from both sides of the equation

54 - 4 = 10 W

50 = 10W

Dividing both sides by the coefficient of W which is 10

5 = W

Therefore, W = 5 inches

Slotting in the value of W in eq 2

L = 2 + 4 (5)

L = 2 + 20

L = 22 inches

Now lets check our answers by slotting in the values of P, L and W in eq 1

54 = 2 (22 + 5)

54 = 2 (27)

54 = 54

Since both sides of the equation are equal, the values of L and W are correct

Hence Length = 22 inches, Width = 5 inches